Question

Medals will be awaded. Simplify Radical Expressions Question

Answer 1

For the numbers, you might want to learn some "divisibility rules". See
https://en.wikipedia.org/wiki/Divisibility_rule#Step-by-step_examples

the idea is to break a number into factors, and look for *pairs* of numbers that can be "pulled out" of the square root

example: \( \sqrt{8}= \sqrt{2 \cdot 2 \cdot 2} \)
there is one pair of 2's that you can take out (and make just a single 2 outside the square root).... \( \sqrt{8}= \sqrt{2 \cdot 2 \cdot 2} = 2 \sqrt{2}\)

for letters it's easier. if you have for example: \( \sqrt{x^3}= \sqrt{x\cdot x \cdot x} = x \sqrt{x} \)
look for pairs.

Answer 2

or
\[ \sqrt{x^5} = \sqrt{ x \cdot x \cdot x \cdot x \cdot x} \]
there are two pairs of x's you can take out (leaving 1 x "inside")
\[ \sqrt{ (x \cdot x) \cdot (x \cdot x) \cdot x}= x\cdot x \sqrt{x} \\
=x^2 \sqrt{x}
\]